*3.1. Characterization of High-Fluence Ion Irradiation*

For the characterization of high-fluence ion irradiation, the depth distributions ν(*x*) of the numbers of displacements per atom (dpa) (damage depth profiles) were calculated. The profiles ν(*x*) were determined by the depth distributions Σ(*x*) of the average numbers of vacancies formed by one ion per path length, which were derived by the computer simulation of the ion interactions with solids using the SRIM code [18]. At not-too-high fluences ν(*x*) ≈ Φ· -(*x*)/*n*0, where the fluence Φ = ϕ·τ is equal to the product of the ion beam flux ϕ and irradiation time τ, *n*<sup>0</sup> is the atomic target concentration [19]. At high fluences, dynamic equilibrium conditions are established, in which the profiles of the concentration of implanted particles and radiation damage become stationary [11]. The stationary damage depth profile νst(*x*) is calculated as follows:

$$\mathbf{v}\_{st}(\mathbf{x}) = \frac{1}{K} \int\_{\mathbf{x}}^{\mathbb{R}d} \Sigma(\mathbf{x}') \cdot d\mathbf{x}',\tag{1}$$

where *Rd* is the depth of the defect production, *K* = *Y* for Ar<sup>+</sup> ion irradiation, *K* = |1−*Y*| for C<sup>+</sup> ion irradiation and *Y* is the sputtering yield.

The calculated stationary profiles νst(*x*) are shown in Figure 1. Based on the calculated profiles of νst(*x*), the thickness *t* of the modified surface layer was estimated.

**Figure 1.** Stationary damage depth profiles under high-fluence ion irradiation.

The value of *t* was determined from the level of 10 dpa. This value of ν was attained over the depths *<sup>x</sup>* <sup>≤</sup> *<sup>R</sup>*d. Unlike for irradiation by gas ions, for C<sup>+</sup> ion irradiation, the thickness of the modified layer increases due to the implanted carbon ions, since the self-sputtering yield (*Y* = 0.21) is less than 1 [20]. For estimating the thickness *t*, the thickness of the deposited carbon was added to the modified layer thickness obtained from νst(*x*).
